Flock model

The flock model illustrates how flocking behavior can emerge when each bird follows three simple rules:

• maintain a minimum distance from other birds to avoid collision
• fly towards the average position of neighbors
• fly in the average direction of neighbors

Defining the core structures

We begin by calling the required packages and defining an agent type representing a bird.

using Agents, Random, LinearAlgebra

mutable struct Bird <: AbstractAgent
    id::Int
    pos::NTuple{2,Float64}
    vel::NTuple{2,Float64}
    speed::Float64
    cohere_factor::Float64
    separation::Float64
    seperate_factor::Float64
    match_factor::Float64
    visual_distance::Float64
end

The fields id and pos are required for every agent. The field vel is required for using move_agent! in ContinuousSpace. speed defines how far the bird travels in the direction defined by vel per step. seperation defines the minimum distance a bird must maintain from its neighbors. visual_distance refers to the distance a bird can see and defines a radius of neighboring birds. The contribution of each rule defined above recieves an importance weight: cohere_factor is the importance of maintaining the average position of neighbors, match_factor is the importance of matching the average trajectory of neighboring birds, and seperate_factor is the importance of maining the minimum distance from neighboring birds.

The function initialize_model generates birds and returns a model object using default values.

function initialize_model(;n_birds=100, speed=1.0, cohere_factor=.25, separation=4.0,
    seperate_factor=.25, match_factor=.01, visual_distance=5.0, dims=(100,100))
    space2d = ContinuousSpace(2; periodic=true, extend=dims)
    model = ABM(Bird, space2d, scheduler=random_activation)
    for _ in 1:n_birds
        vel = Tuple(rand(2)*2 .- 1)
        add_agent!(
            model, vel, speed, cohere_factor,separation, seperate_factor,
            match_factor,visual_distance
        )
    end
    index!(model)
    return model
end

initialize_model (generic function with 1 method)

Defining the agent_step!

agent_step! is the primary function called for each step and computes velocity according to the three rules defined above.

function agent_step!(bird, model)
    # Obtain the ids of neibhors within the bird's visual distance
    ids = space_neighbors(bird, model, bird.visual_distance)
    # Compute velocity based on rules defined above
    bird.vel = (bird.vel .+
        cohere(bird, model, ids) .+
        seperate(bird, model, ids) .+
        match(bird, model, ids))./2
    bird.vel = bird.vel ./ norm(bird.vel)
    # Move bird according to new velocity and speed
    move_agent!(bird, model, bird.speed)
end

distance(a1, a2) = sqrt(sum((a1.pos .- a2.pos).^2))

get_heading(a1, a2) = a1.pos .- a2.pos

get_heading (generic function with 1 method)

cohere computes the average position of neighboring birds, weighted by importance

function cohere(bird, model, ids)
    N = max(length(ids), 1)
    birds = model.agents
    coherence = (0.0,0.0)
    for id in ids
        coherence = coherence .+ get_heading(birds[id], bird)
    end
    return coherence./N.*bird.cohere_factor
end

cohere (generic function with 1 method)

seperate repells the bird away from neighboring birds

function seperate(bird, model, ids)
    seperation_vec = (0.0,0.0)
    N = max(length(ids), 1)
    birds = model.agents
    for id in ids
        neighbor = birds[id]
        if distance(bird, neighbor) < bird.separation
            seperation_vec = seperation_vec .- get_heading(neighbor, bird)
        end
    end
    return seperation_vec./N.*bird.seperate_factor
end

seperate (generic function with 1 method)

match computes the average trajectory of neighboring birds, weighted by importance

function match(bird, model, ids)
    match_vector = (0.0, 0.0)
    N = max(length(ids), 1)
    birds = model.agents
    for id in ids
        match_vector = match_vector .+ birds[id].vel
    end
    return match_vector./N.*bird.match_factor
end

match (generic function with 1 method)

Running the model

Random.seed!(23182)
n_steps = 500
model = initialize_model()
step!(model, agent_step!, n_steps)

Plotting the birds

The great thing about plotabm is its flexibility. We can incorporate the direction of the birds when plotting them, by making the "marker" function am create a Shape: a triangle with same orientation as the bird's velocity. It is as simple as defining the following function:

function bird_triangle(b::Bird)
    φ = atan(b.vel[2], b.vel[1])
    xs = [(i ∈ (0, 3) ? 2 : 1)*cos(i*2π/3 + φ) for i in 0:3]
    ys = [(i ∈ (0, 3) ? 2 : 1)*sin(i*2π/3 + φ) for i in 0:3]
    Shape(xs, ys)
end

bird_triangle (generic function with 1 method)

And here is the animation

using AgentsPlots, Plots
Random.seed!(23182)
model = initialize_model()
anim = @animate for i in 1:1000
    step!(model, agent_step!, 1)
    p1 = plotabm(model; am = bird_triangle, as = 10)
    title!(p1, "step $(i)")
end
gif(anim, "flock.gif", fps=30)